A wine bottle and a grape with a few bits and bytes to provide a logo for this assignment

This paper explores which chemical components influence wine quality with the method of ‘Exploratory Data Analysis’ using the R programming language. It is part of Udacity Data Analyst Nanodegree. It is written as an R-Markdown file and provides a stream-of-contiousness analysis of the data as well as a ‘Final Plots’ section at the end which is somewhat more cut-to-the-chase.

In the data set at hand, about 5000 white wines are scored by professionals (0 being bad, 10 being excellent) and the chemical properties are recorded. After doing some preparations and loading the data set, we will go through each variable one-by-one.

1 Preparations

First, we load libraries and define some functions to achieve a unique ‘look and feel’ and some shortcuts for the plotting styles most commonly used in this project.

library(ggplot2) # plotting 
library(gridExtra) # arranging multiple plots in one figure
library(grid) 
library(tidyr) # cleaning & data re-shaping
library(dplyr)
library(scales) # advanced manipulating of axes and color indicators
library(GGally) # scatterplot matrixes

# Helper function to create a beautiful ggplot2 histogram object
ggplot_hist <- function(data, x, binwidth, xlab="", title="", xscale=NA,
      ylab="", fill=NA, median=T, facet=NA, ncol=1, nrow=1,
      coordflip=F, fillname=NA) {
  # Environment is needed for proper evaluation of eas wrapper in context
  # of variables supplied to this function
  e <- environment()
  # Standard ggplot2 object with or without color facetting
  if (!is.na(fill))
    p <- ggplot(data=data, aes(x=data[,x], fill=data[,fill]), environment=e)
    if (!is.na(fillname))
      p <- p + scale_fill_discrete(name=fillname)
  else
    p <- ggplot(data=data, aes(x=data[,x]), environment=e)
  # Histogram with labels and title
  p <- p + 
      geom_histogram(binwidth=binwidth, alpha=0.5, position='identity') + 
      labs(x=xlab, y=ylab) + ggtitle(title)
  # Add marker for median if requested
  if (median == T)
    p <- p + geom_vline(x=mean(data[,x]))
  # Set scaling and breaks on axes if requested
  if (length(xscale) == 3) 
    p <- p + scale_x_continuous(limits = xscale[1:2],
                                breaks = seq(xscale[1], xscale[2], xscale[3]))
  # Flip coords if requested
  if (coordflip == T)
    p <- p + coord_flip()
  # Facet with number of rows / columns, if requested
  if (!is.na(facet))
    p <- p + facet_wrap(facet, ncol=ncol, nrow=nrow)
  # Return for potential further processing
  return(p)
}

# Function to plot histograms with a second view showing rel. frequency
# and normal curve overlay
ggplot_normdist <- function(data, x, binwidth, xlab, title, xscale=NA, ylab) {
  # Environment is needed for proper evaluation of eas wrapper in context
  # of variables supplied to this function
  e <- environment()
  # Normal curve overlay
  p1 <- ggplot(data=data, aes(x=data[,x]), environment=e) +
    # Histogram with density variable (gives relative frequencies)
    geom_histogram(aes(y = ..density..), binwidth=binwidth, alpha = 0.2) + 
    # Add normal curve overlay
    stat_function(geom="line", fun=dnorm, arg=list(mean=mean(data[,x]),
                                                   sd=sd(data[,x]))) + 
    # Add marker for mean
    geom_vline(x=mean(data[,x])) + 
    # No x-axis (shown by main plot)
    theme(axis.ticks.x = element_blank(), axis.text.x = element_blank()) +
    # Fixed label for y-axis, x-label given by parameter
    labs(y="Relative Frequency", x=xlab) + 
    # Manipulate margins to "attach" to below main graph
    theme(plot.margin = unit(c(15,5,-20,6), unit="points"),
          axis.title.y = element_text(vjust =0.25)) +
    ggtitle(title)
  # Change scale of x-axis, if requested
  if (length(xscale) == 3) 
    p1 <- p1 + scale_x_continuous(limits = xscale[1:2],
                                  breaks = seq(xscale[1], xscale[2], xscale[3]))
  # Main plot below is a standard histogram as given by ggplot_hist helper
  p2 <- ggplot_hist(data, x, binwidth, xlab, "", xscale, ylab) + 
    # but we need to modify the margin to fit it together with the plot above
    theme(plot.margin = unit(c(0,5,1,1), unit="points"))
  grid.arrange(p1, p2, heights=c(0.2,0.4))
}

# Function to create a scatter plot to examine for corellation
ggplot_corr <- function(data, x, y, xlab, ylab, xscale=NA, yscale=NA, title) {
  # Environment is needed for proper evaluation of eas wrapper in context
  # of variables supplied to this function
  e <- environment()
  # Jittered scatterplot with alpha = 0.1
  p <- ggplot(data=data, aes(x=data[,x], y=data[,y]), environment=e) + 
          geom_jitter(alpha=0.1) + 
          # Linear Smoother to examine corellation
          stat_smooth(geom = "smooth", method = "lm") +
          # Labels & Title
          labs(x=xlab, y=ylab)  + 
          ggtitle(title)
  # Scale x axis if required
  if (length(xscale) == 3)
    p <- p + scale_x_continuous(limits = xscale[1:2],
                                breaks = seq(xscale[1], xscale[2], xscale[3]))
  # Scale y axis if required
  if (length(yscale) == 3)
    p <- p + scale_y_continuous(limits = yscale[1:2],
                                breaks = seq(yscale[1], yscale[2], yscale[3]))
  return(p)
}

# Function to create a bunch of horizontally stacked box plots
ggplot_boxplot <- function(data, x, y, xlab="", title="", yscale=NA, ylab="",
      facet=NA, ncol=1, nrow=1, smooth=T, fill=NA, fillname="") {
  # Environment is needed for proper evaluation of eas wrapper in context
  # of variables supplied to this function
  e <- environment()
  # Filled box plots (or not)
  if (!is.na(fill))
    p <- ggplot(data=data, aes(x=data[,x], y=data[,y], fill=data[,fill]),
                environment=e) + 
      scale_fill_discrete(name=fillname)
  else
    p <- ggplot(data=data, aes(x=data[,x], y=data[,y]), environment=e)
  p <- p + geom_boxplot(position='dodge') +
          labs(x=xlab, y=ylab) + ggtitle(title)
  # Add smoother between horizontally stacked box plots if required
  if (smooth == T)
    p <- p + geom_smooth(method="lm", aes(group=1))
  # Scale y-axis if required
  if (length(yscale) == 3) 
    p <- p + scale_y_continuous(limits = yscale[1:2],
                                breaks = seq(yscale[1], yscale[2], yscale[3]))
  # Facet plots horizontally / vertically
  if (!is.na(facet))
    p <- p + facet_wrap(facet, ncol=ncol, nrow=nrow)
  return(p)
}

2 First Observations

We load the data and assess its structure:

# load data
setwd("h:/Dokumente/GitHub/2015_Data_Analyst_Project_4/")
wine <- read.csv("project/wineQualityWhites.csv")
# read and display data structure
str(wine)
## 'data.frame':    4898 obs. of  13 variables:
##  $ X                   : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ fixed.acidity       : num  7 6.3 8.1 7.2 7.2 8.1 6.2 7 6.3 8.1 ...
##  $ volatile.acidity    : num  0.27 0.3 0.28 0.23 0.23 0.28 0.32 0.27 0.3 0.22 ...
##  $ citric.acid         : num  0.36 0.34 0.4 0.32 0.32 0.4 0.16 0.36 0.34 0.43 ...
##  $ residual.sugar      : num  20.7 1.6 6.9 8.5 8.5 6.9 7 20.7 1.6 1.5 ...
##  $ chlorides           : num  0.045 0.049 0.05 0.058 0.058 0.05 0.045 0.045 0.049 0.044 ...
##  $ free.sulfur.dioxide : num  45 14 30 47 47 30 30 45 14 28 ...
##  $ total.sulfur.dioxide: num  170 132 97 186 186 97 136 170 132 129 ...
##  $ density             : num  1.001 0.994 0.995 0.996 0.996 ...
##  $ pH                  : num  3 3.3 3.26 3.19 3.19 3.26 3.18 3 3.3 3.22 ...
##  $ sulphates           : num  0.45 0.49 0.44 0.4 0.4 0.44 0.47 0.45 0.49 0.45 ...
##  $ alcohol             : num  8.8 9.5 10.1 9.9 9.9 10.1 9.6 8.8 9.5 11 ...
##  $ quality             : int  6 6 6 6 6 6 6 6 6 6 ...
dim(wine)
## [1] 4898   13

Seems like no addtitional post-processing will be necessary. quality may be more useful as a factor in certain use cases (we will keep this in mind). We can also see, that there are 4898 observations and 15 variables.

Let’s look at the distribution of the key chemical parameters one-by-one by plotting their distribution and their statistical (summary(...)) properties.

2.1 Fixed Acidity (Tartaric Acid) in \(\text{g}/\text{l}\)

Most acids involved with wine are fixed or nonvolatile (do not evaporate readily).

Fixed acidity seems normally distributed (\(\mu = 6.800 \frac{\text{g}}{\text{l}}, \sigma = 0.843 \frac{\text{g}}{\text{dm}^3}\)).

summary(wine$fixed.acidity)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.800   6.300   6.800   6.855   7.300  14.200
sd(wine$fixed.acidity) # Standard deviation
## [1] 0.8438682
ggplot_normdist(
    data=wine, x="fixed.acidity", binwidth=0.1, xscale=c(3.5, 11, 0.5),
    title="Distribution of fixed acidity (tartaric acid)",
    xlab="Fixed acidity (tartaric acid) in g/l",
    ylab="Number of wines with this fixed acidity"
  )

2.2 Volatile Acidity (Acetic Acid) in \(\text{g}/\text{l}\)

The amount of acetic acid in wine, which at too high of levels can lead to an unpleasant, vinegar taste.

Volatile acids seem to be presentin much lower quantities than fixed acids by an order of magnitude, their distribution (\(\mu = 0.2782 \frac{\text{g}}{\text{l}}, \sigma = 0.1008 \frac{\text{g}}{\text{dm}^3}\)) is slightly skewed to the left.

summary(wine$volatile.acidity)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0800  0.2100  0.2600  0.2782  0.3200  1.1000
sd(wine$volatile.acidity)
## [1] 0.1007945
ggplot_hist(
     data=wine, x="volatile.acidity", binwidth=0.02, xscale=c(0, 0.9, 0.05), 
     title="Distribution of volatile acidity (acetic acid)",
     xlab="Volatile acidity (acetic acid) in g/l",
     ylab="Number of wines with this volatile acidity"
  )

2.3 Citric Acid in \(\text{g}/\text{l}\)

Found in small quantities, citric acid can add ‘freshness’ and flavor to wines.

The amount of citric acidity seems to follow a slightly higher, but otherwise comparable distribution to the volatile acidity (\(\mu = 0.3342 \frac{\text{g}}{\text{l}}, \sigma = 0.1210 \frac{\text{g}}{\text{dm}^3}\)). Left-skewedness seems to be smaller.

summary(wine$citric.acid)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.2700  0.3200  0.3342  0.3900  1.6600
sd(wine$citric.acid)
## [1] 0.1210198
ggplot_hist(
     data=wine, x="citric.acid", binwidth=0.02, xscale=c(0, 1.4, 0.1),
     title="Distribution of citric acidity",
     xlab="Cidric acid in g/l",
     ylab="Number of wines with this citric acidity"
  )

2.4 Multivariate Analysis: Acidity Values

The following graph shows the relationship between the acidity distributions. Notice how fixed acidity is broader spread and generally higher than citric and volatile acidity.

# Create a dataframe with the columns acidtype, acidvalue and fill it 
# with all of the values for citric.acid, volatile.acidity,
# fixed.acidity for all of the wines ...
wineacids <- wine %>%                                                                                                        
  dplyr::select(citric.acid, volatile.acidity, fixed.acidity) %>%
  tidyr::gather("acidtype","acidvalue", 1:3)

# ... then plot those as overlayed histograms
ggplot_hist(
     data=wineacids, x="acidvalue", binwidth=0.1, xscale=c(0, 11, 0.5),
     xlab="Acidity in g/dm³",
     title="Distribution of all acidities",
     ylab="Number of wines with this acidity",
     fill="acidtype", fillname="Type of Acid", median=F
  )

Does one type of acid come with another type of acid? That is, are any two of the acidity values corellated?

cor(wine[, c("fixed.acidity", "volatile.acidity", "citric.acid")],
    wine[, c("fixed.acidity", "volatile.acidity", "citric.acid")])
##                  fixed.acidity volatile.acidity citric.acid
## fixed.acidity       1.00000000      -0.02269729   0.2891807
## volatile.acidity   -0.02269729       1.00000000  -0.1494718
## citric.acid         0.28918070      -0.14947181   1.0000000

We can find that fixed acidity and citric acidity are slightly positively corellated (\(r = 0.289\)), that means, where more fixed acidity is present, also more citric acidity is present.

The next plot shows this, but notice the significant spread in the middle of both acidity distributions.

ggplot_corr(
    data=wine, x="fixed.acidity", y="citric.acid", 
    xscale=c(3.5, 11, 0.5), yscale=c(0, 1.4, 0.1),
    xlab="Fixed acidity (tartaric acid) in g/l",
    ylab="Citric acidity in g/l",
    title="Fixed acidity vs. citric acidity"
  )

However, we find that volatile acidity is slightly negatively corellated with both types of acidity (\(r_\text{fixed} = -0.0227, r_\text{citric} = -0.1495\) - hinting at that for wines with volatile acidity, less of the other two kinds of acids are present. The next two plots show this relationship.

p1 <- ggplot_corr(
    data=wine, x="volatile.acidity", y="fixed.acidity", 
    xscale=c(0, 0.9, 0.05), yscale=c(3.5, 11, 0.5), 
    xlab="Volatile acidity (acetic acid) in g/l",
    ylab="Fixed acidity (tartaric acid) in g/l",
    title="Volatile acidity vs. fixed acidity"
  )
p2 <- ggplot_corr(
    data=wine, x="volatile.acidity", y="citric.acid", 
    xscale=c(0, 0.9, 0.05), yscale=c(0, 1.4, 0.1),
    xlab="Volatile acidity (acetic acid) in g/l",
    ylab="Citric acidity in g/l",
    title="Volatile acidity vs. citric acidity"
  )
grid.arrange(p1, p2, nrow=1)

2.5 pH

… describes how acidic or basic a wine is on a scale from 0 (very acidic) to 14 (very basic); most wines are between 3-4 on the pH scale.

As expected, we find the pH value distribution with a mean between 3-4 (\(\mu = 3.188\)), most likely influenced by the most prevalent acid (fixed acids).

summary(wine$pH)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.720   3.090   3.180   3.188   3.280   3.820
sd(wine$pH)
## [1] 0.1510006
ggplot_normdist(
     data=wine, x="pH", binwidth=0.02, xscale=c(2.6, 4.0, 0.2),
     xlab="pH value",
     ylab="Number of wines with this pH value",
     title="pH value"
  )

2.6 Multivariate Analysis: pH vs. Acidity

pH is a measure for acidity, but are pH value and the concentration-values of each acid corellated or does any of the acid concentractions have a particulary strong influence? We also create a new “sum-by-concentration” variable acidtity where we just add the concentration of all acids.

We find, as expected, the strongest (negative) corellation between pH and the most prevalent, fixed, acidity (\(r = -0.4258\)). Calculating \(r^2\) or for how much variability in pH this acidity accounts, we get \(r^2 = 0.1814\), which is rather small, but we have to take into account the chemical properties: in a wine, there might be basic molecules which counteract acid components and drive the pH up.

# Create aggregate (sum) variable of all acidities
wine$acidity <- wine$fixed.acidity + wine$volatile.acidity + wine$citric.acid

# Pearsons R
cor(wine[, c("fixed.acidity", "volatile.acidity", "citric.acid", "acidity")],
    wine$pH)
##                         [,1]
## fixed.acidity    -0.42585829
## volatile.acidity -0.03191537
## citric.acid      -0.16374821
## acidity          -0.43065133
# R^2 - For how much variability in pH the acidity variables account 
cor(wine[, c("fixed.acidity", "volatile.acidity", "citric.acid", "acidity")],
    wine$pH)^2
##                         [,1]
## fixed.acidity    0.181355284
## volatile.acidity 0.001018591
## citric.acid      0.026813477
## acidity          0.185460569
p1 <- ggplot_corr(
    data=wine, x="fixed.acidity", y="pH",
    xscale=c(3.5, 11, 0.5), yscale=c(2.6, 4.0, 0.2),
    xlab="Fixed acidity (tartaric acid) in g/l",
    ylab="pH",
    title="Fixed acidity vs. pH"
  )
p2 <- ggplot_corr(
    data=wine, x="volatile.acidity", y="pH", 
    xscale=c(0, 0.9, 0.05), yscale=c(2.6, 4.0, 0.2),
    xlab="Volatile acidity (acetic acid) in g/l",
    ylab="pH",
    title="Volatile acidity vs. pH"
  )
p3 <- ggplot_corr(
    data=wine, x="citric.acid", y="pH", 
    xscale=c(0, 1.4, 0.1), yscale=c(2.6, 4.0, 0.2),
    xlab="Citric acidity in g/l",
    ylab="pH",
    title="Citric acidity vs. pH"
  )
p4 <- ggplot_corr(
    data=wine, x="acidity", y="pH", 
    xscale=c(3.5, 12, 0.5), yscale=c(2.6, 4.0, 0.2),
    xlab="Sum of acid concentrations in g/l",
    ylab="pH",
    title="'Total' acidity vs. citric acidity"
  )
grid.arrange(p1, p2, p3, p4, nrow=2)

2.7 Chloride Concentration in \(\text{g}/\text{l}\)

… the amount of salt in the wine.

The amount of salt in the wine seems normally distributed at first (\(\mu = 0.0457 \frac{\text{g}}{\text{l}}, \sigma = 0.02184 \frac{\text{g}}{\text{l}}\)) but has an extremely ‘long tail’ on the right which would ‘stretch’ a fitted bell curve. Delimited by dashed lines in belows graph is the 90% confidence interval which the largest part of the bell curve would cover. It will be interesting to see, if/how those outliers affect wine quality.

summary(wine$chlorides)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00900 0.03600 0.04300 0.04577 0.05000 0.34600
sd(wine$chlorides)
## [1] 0.02184797
quantile(wine$chlorides, 3/4)
##  75% 
## 0.05
ggplot_hist(
     data=wine, x="chlorides", binwidth=0.002, xscale=c(0, 0.2, 0.01),
     title="Distribution of chlorides (salts)",                                                                              
     xlab="Chlorides in g/l",
     ylab="Number of wines with this amount of chlorides"
  ) + 
  geom_vline(x=quantile(wine$chlorides, 0.05), linetype="dashed") + 
  geom_vline(x=quantile(wine$chlorides, 0.95), linetype="dashed")

2.8 Free Sulfur Dioxide in \(\text{mg}/\text{l}\)

The free form of SO2 exists in equilibrium between molecular SO2 (as a dissolved gas) and bisulfite ion; it prevents microbial growth and the oxidation of wine.

Also for this chemical property, there are a few outliers on the right, making the fitted normal distribution curve (\(\mu = 35.31 \frac{\text{mg}}{\text{l}}, \sigma = 17.0071 \frac{\text{mg}}{\text{l}}\)) slightly more left-skewed and broader. There is one extreme outlier >150 mg/l which we will just tabulate and not include in the graph

summary(wine$free.sulfur.dioxide)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.00   23.00   34.00   35.31   46.00  289.00
sd(wine$free.sulfur.dioxide)
## [1] 17.00714
subset(wine, free.sulfur.dioxide > 150)
##         X fixed.acidity volatile.acidity citric.acid residual.sugar
## 4746 4746           6.1             0.26        0.25            2.9
##      chlorides free.sulfur.dioxide total.sulfur.dioxide density   pH
## 4746     0.047                 289                  440 0.99314 3.44
##      sulphates alcohol quality acidity
## 4746      0.64    10.5       3    6.61
ggplot_normdist(
     data=wine, x="free.sulfur.dioxide", binwidth=2, xscale=c(0, 150, 10), 
     title="Free sulfur dioxide",
     xlab="Free sulfur dioxide in mg/dm³",
     ylab="Number of wines with this amount of free SO2"
  )

2.9 Total Sulfur Dioxide in \(\text{mg}/\text{l}\)

Amount of free and bound forms of S02; in low concentrations, SO2 is mostly undetectable in wine, but at free SO2 concentrations over 50ppm, SO2 becomes evident in the nose and taste of wine.

The total sulfur dioxide distribution (\(\mu = 138.4 \frac{\text{g}}{\text{l}}, \sigma = 42.498 \frac{\text{g}}{\text{l}}\)) shows that the average total sulfur dioxide content is about 3 times higher than the average free sulfur dioxide content. The left-skewedness is less noticable than for free sulfur dioxide contents and the “long-tail” on the right is shorter.

summary(wine$total.sulfur.dioxide)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     9.0   108.0   134.0   138.4   167.0   440.0
sd(wine$total.sulfur.dioxide)
## [1] 42.49806
ggplot_normdist(
     data=wine, x="total.sulfur.dioxide", binwidth=2, xscale=c(0, 400, 10),
     title="Total sulfur dioxide",
     xlab="Total sulfur dioxide in mg/dm³",
     ylab="Number of wines with this amount of total SO2"
  )

2.10 Multivariate Analysis: Total vs. Free Sulfur Dioxide

Analyzing the corellation between total and free sulfur dioxide content we find that with an increase of total sulfur dioxide by 1 mg/l, free sulfur dioxide increases by \(r = 0.6155 \frac{\text{mg}}{\text{l}}\) and mostly accounts for the majority of sulfur dioxide increase. However, variability of the free sulfur dioxide content increases with a higher total sulfur dioxide content.

cor(wine$total.sulfur.dioxide, wine$free.sulfur.dioxide)
## [1] 0.615501
ggplot_corr(
    data=wine, x="total.sulfur.dioxide", y="free.sulfur.dioxide", 
    xscale=c(0, 300, 20), yscale=c(0, 160, 20),
    xlab="Total sulfur dioxide in mg/dm³",
    ylab="Free sulfur dioxide in mg/dm³",
    title="Total sulfur dioxide vs. free sulfur dioxide"
  )

2.11 Sulphates (\(\text{g}/\text{l}\))

… a wine additive which can contribute to sulfur dioxide gas (S02) levels, wich acts as an antimicrobial and antioxidant.

We see a slightly left-skewed distribution of sulphate content ($= 0.4898 , $).

summary(wine$sulphates)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2200  0.4100  0.4700  0.4898  0.5500  1.0800
sd(wine$sulphates)
## [1] 0.1141258
ggplot_hist(
     data=wine, x="sulphates", binwidth=0.01, xscale=c(0.2, 1.000, 0.05),
     title="Sulphates", 
     xlab="Sulphates in the wine in g/dm³",
     ylab="Number of wines with that amount of sulphates"
  )

2.12 Multivariate Analysis: Sulphates vs. Total Sulfur Dioxide

Let’s verify to which extent the variable description holds true and how much sulfates really contribute to ‘unpleasant’ SO2 levels. Calculating the \(r\), we find just \(r = 0.1345\) and \(r^2 = 0.0181\), showing that variability of the sulphate only describes 1.8% percent of the variability in the sulfur dioxide level and therefore is not a very good indicator for total sulfur dioxide level. The corellation for free sulfur dioxide is even lower (\(r_\text{free} = 0.0592\)).

cor(wine$sulphates, wine$total.sulfur.dioxide)
## [1] 0.1345624
cor(wine$sulphates, wine$total.sulfur.dioxide)^2
## [1] 0.01810703
cor(wine$sulphates, wine$free.sulfur.dioxide)
## [1] 0.05921725
ggplot_corr(
    data=wine, x="sulphates", y="total.sulfur.dioxide", 
    xscale=c(0.2, 1.000, 0.05), yscale=c(0, 300, 20),
    xlab="Sulphates in the wine in g/dm³",
    ylab="Total sulfur dioxide in mg/dm³",
    title="Sulphates vs. total sulfur dioxide"
  )

2.13 Residual Sugar

The amount of sugar remaining after fermentation stops, it’s rare to find wines with less than 1 gram/liter and wines with greater than 45 grams/liter are considered sweet.

The distribution of sugar in the wine is non-normal (\(\mu = 6.391 \frac{g}{l}\)). There seem to be several different local maxima, the largest at around 1.5 g/l, smaller ones at 4.5 g/l, 6.3 g/l and 8 g/l, potentially signifying the different wine flavours (sweet, dry, etc.) - we will get back to those later.

There is only one sweet wine (with sugar content of over 45 g/l), which we will not show but tabulate. It seems to be a wine rated slightly above average (score 6).

summary(wine$residual.sugar)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.600   1.700   5.200   6.391   9.900  65.800
subset(wine, residual.sugar > 45) # tabulate the only sweet wine
##         X fixed.acidity volatile.acidity citric.acid residual.sugar
## 2782 2782           7.8            0.965         0.6           65.8
##      chlorides free.sulfur.dioxide total.sulfur.dioxide density   pH
## 2782     0.074                   8                  160 1.03898 3.39
##      sulphates alcohol quality acidity
## 2782      0.69    11.7       6   9.365
ggplot_hist(
     data=wine, x="residual.sugar", binwidth=0.2, xscale=c(0, 45, 2),
     title="Distribution of residual sugar (non-sweet wines)",
     xlab="Residual sugar in g/dm³",
     ylab="Number of wines with this residual sugar content"
  )

2.14 Alcohol Content in %

As the sugar content does, the alcohol also is a distribution with several local maxima (\(\mu = 10.5%, \text{max} = 14.2%, \text{min} = 8.0%\)). It is to be expected, that each wine flavor on the market contributes to the overall distribution with their signature distributions.

summary(wine$alcohol)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.00    9.50   10.40   10.51   11.40   14.20
ggplot_hist(
     data=wine, x="alcohol", binwidth=0.1, xscale=c(8, 14, 0.5), 
     title="Alcohol level", 
     xlab="Alcohol level in % by volume",
     ylab="Number of wines with that alcohol level"
  )

2.15 Multivariate Analysis: Residual Sugar vs. Alcohol

Gestation creates alcohol from sugar, therefore, with more alcohol in the wine, we expect less sugar; indeed, the values are negatively corellated (\(r = -0.4506\)). The graph below shows that indeed, a higher residual sugar content leads to less alcohol, but we also note, that the spread of the alcohol content is much higher for wines with lower sugar content, suggesting perhaps, that some wines may have not enough sugar to turn into alcohol to begin with.

cor(wine$residual.sugar, wine$alcohol)
## [1] -0.4506312
ggplot_corr(
    data=wine, x="residual.sugar", y="alcohol", 
    xscale=c(0, 45, 2), yscale=c(8, 14, 0.5),
    xlab="Residual sugar in g/dm³", 
    ylab="Alcohol level in % by volume",
    title="Residual sugar vs. alcohol level"
  )
## Warning: Removed 3 rows containing missing values (stat_smooth).
## Warning: Removed 7 rows containing missing values (geom_point).
## Warning: Removed 8 rows containing missing values (geom_path).

2.16 Density in \(\text{kg}/\text{l}\)

The density of water is close to that of water depending on the percent alcohol and sugar content.

Wine density is somewhat tightly normally distributed around the density of water ($= 0.9940 , = 2.9 ).

summary(wine$density)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9871  0.9917  0.9937  0.9940  0.9961  1.0390
sd(wine$density)
## [1] 0.002990907
ggplot_normdist(
     data=wine, x="density", binwidth=0.0005, xscale=c(0.985, 1.005, 0.005),
     title="Density",
     xlab="Density of the wine in kg/l",
     ylab="Number of wines with that density"
  )

2.17 Multivariate Analysis: Density vs. Sugar & Alcohol Level

Verifying the statement of the variable description about the density to be influenced by residual sugar and alcohol content, we analyze the corellation and find \(r_\text{residual.sugar} = 0.8390, r_\text{alcohol} = -0.78013\).

Checking \(r^2\), we find that 70.3% of the variability of density is explained by the variability in residual sugar, 60.8% of the variability of density is explained by the variabilit in alcohol; since these two variables are highly coreallated, we could not use them both in a linear model explaining the density variable.

cor(wine$density, wine[, c("residual.sugar", "alcohol")])
##      residual.sugar    alcohol
## [1,]      0.8389665 -0.7801376
cor(wine$density, wine[, c("residual.sugar", "alcohol")])^2
##      residual.sugar   alcohol
## [1,]      0.7038647 0.6086147
p1 <- ggplot_corr(
    data=wine, x="alcohol", y="density", 
    xscale=c(8, 14, 0.5), yscale=c(0.985, 1.005, 0.005),
    xlab="Alcohol level in % by volume",
    ylab="Density in g/cm³",
    title="Alcohol vs. Density"
  )
p2 <- ggplot_corr(
    data=wine, x="residual.sugar", y="density", 
    xscale=c(0, 45, 2), yscale=c(0.985, 1.005, 0.005),
    xlab="Residual sugar in g/dm³",
    ylab="Density in g/cm³",
    title="Residual Sugar vs. Density"
  )

grid.arrange(p1, p2, nrow=1)

2.18 Output Variable: Quality based on Sensory Data (0-10)

The following graph shows the overall distribution of the score that was given to the wines. It ranges from 3 to 9, with 20 wines being in the worst category (3), 5 in the best (9) and most wines (2198) scoring a “6” slightly above average (5.86) and the mid-point value that could be avarded (5), potentially showing a psychological bias of the wine testers to slightly overscore wines.

summary(wine$quality)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.000   5.000   6.000   5.878   6.000   9.000
table(wine$quality)
## 
##    3    4    5    6    7    8    9 
##   20  163 1457 2198  880  175    5
ggplot_hist(
     data=wine, x="quality", binwidth=1, xscale=c(0, 10, 1),
     title="Quality Score ",
     xlab="Quality Score (0-10)",
     ylab="Number of Wines having that Quality"
  )

2.19 Categorical Variable: Wine Flavor

We create the following categorical variable to classify wines according to their flavor based on existing EU regulations:

  • wines with max. 4 g/l residual sugar are considered ‘classical-dry’, acidity should be not less than 2 g/l below sugar content
  • wines with max. 9 g/l residual sugar are considered ‘dry’, acidity should be not less than 2 g/l below sugar content
  • wines with max. 18 g/l residual sugar content are considered ‘half-dry’, acidity should be not less than 10 g/l below sugar content
  • wines with max. 45 g/l residual sugar content are considered ‘semi-sweet’
  • wines above 45 g/l residual sugar content are considered ‘sweet’

There are many (classical-)dry wines, less sweet wines, only a few semi-sweet wine and only one single sweet wine.

# Create categorical variable for "wine flavor" according to EU trade 
# specifications; variable is depending on acidity and residual sugar
wine$flavor <- 
      ifelse(wine$residual.sugar <= 4 & wine$acidity >= wine$residual.sugar-2,
              "classical-dry",
      ifelse(wine$residual.sugar <= 9 & wine$acidity >= wine$residual.sugar-2,
              "dry",
      ifelse(wine$residual.sugar <= 18 & wine$acidity >= wine$residual.sugar-10,
              "half-dry",
      ifelse(wine$residual.sugar <= 45, "semi-sweet",
      ifelse(wine$residual.sugar > 45, "sweet",
      "unclassified"
      )))))


# Show how many wines have each flavor
table(wine$flavor)
## 
## classical-dry           dry      half-dry    semi-sweet         sweet 
##          2097          1414          1246           140             1

The following graph visualizes the classification by showing residual sugar level and acidity level. The flavor the wine is assigned is color-coded. One can see a slight “diagonal slope” at each cut-off-point between clusters signifying one particular flavor type. These are due to the restrictions put on the acidity level.

# Plot relationship of wine flavor depending on acidity and residual sugar
ggplot(data=wine, aes(x=residual.sugar, y=acidity, colour=flavor)) +  
  geom_jitter(alpha=0.5) + 
  labs(x="Residual sugar in g/l", y="'Total' acidity in g/l") + 
  ggtitle("Classification of wines according to EU law") +
  scale_x_continuous(limits=c(0, 66), breaks = seq(0, 66, 5)) + 
  scale_y_continuous(limits=c(3.5, 15), breaks=seq(3.5, 15, 0.5)) + 
  scale_colour_discrete(name="Flavor")

Finally, we show the sugar content distribution of each wine flavor as a histogram. It is now evident, that the local maxima in the aggregated histogram are due to treating all the wines in “one bucket”. Within the sugar content distribution of their wine flavor, the distributions are much more uniform.

ggplot_hist(
     data=wine, x="residual.sugar", binwidth=0.2, xscale=c(0, 45, 2),
     fill="flavor", fillname="Wine Flavor",
     title="Distribution of residual sugar (non-sweet wines)",
     xlab="Residual sugar in g/dm³",
     ylab="Number of wines with this residual sugar content"
  )

2.20 Scatterplot Matrix

In order to explore the data further, we use a scatterplot matrix which shows

  • a graph for the relationship between any two variables in the lower left triangle, using a scatterplot for numerical data
  • rows/columns that involves a categorical variable showing facetted plots
  • distributions of single variables along the diagonale
set.seed(1836)
winematrix <- wine[, c(2:15)]
ggpairs(data=winematrix[sample.int(nrow(winematrix), 1000), ],
        title="Relationship between any two variables",
        alpha=0.05)

2.20.1 Confirmation of previous findings (little surprises)

First, we can-re-confirm our previous findings.

cor(wine$acidity, wine[, c("fixed.acidity", "volatile.acidity", "citric.acid")])
##      fixed.acidity volatile.acidity citric.acid
## [1,]     0.9871787       0.07157062   0.3941434

Negative corellation; acidity is defined as the sum-of-weight of all acids; with fixed acids and citrics acids usually dominating over volatile acids, the corellation here is stronger.

cor(wine$pH, wine[, c("acidity", "fixed.acidity",
                      "volatile.acidity", "citric.acid")])
##         acidity fixed.acidity volatile.acidity citric.acid
## [1,] -0.4306513    -0.4258583      -0.03191537  -0.1637482

Negative corellation between pH and all types of acidity; however, corellation between acidity and pH can never be 1.0 because pH should also take basic chemical components into account. Thus, also corellation between pH and any specific type of acidity is lower than corellation between the variable acidity and the corresponding type of acidity.

cor(wine$total.sulfur.dioxide, wine$free.sulfur.dioxide)
## [1] 0.615501

Strong positive corellation because free sulfur dioxide makes out the majority of all sulfur dioxides.

cor(wine$sulphates, wine$total.sulfur.dioxide)
## [1] 0.1345624

Weak positive corellation, as the description of sulphates suggests, sulphates lead to the creation of SO2 levels.

cor(wine$alcohol, wine$residual.sugar)
## [1] -0.4506312

Strong negative corellation because of chemical process of alcohol gestation (sugar is converted to alcohol).

cor(wine$residual.sugar, wine$density)
## [1] 0.8389665

Strong positive corellation, additional sugar in the fluid leads to a higher density than no sugar.

cor(wine$free.sulfur.dioxide, wine$total.sulfur.dioxide)
## [1] 0.615501

Strong positive corellation, because free sulfur dioxide is the major part of total sulfur dioxide.

2.20.2 New Findings Concerning Chemical Properties

cor(wine$residual.sugar, wine$free.sulfur.dioxide)
## [1] 0.2990984

Weak positive corellation – Free sulfur dioxide ‘prevents microbial growth’, therefore might constrain alcohol gestation and result in more remaining residual sugar.

cor(wine$chlorides, wine$alcohol)
## [1] -0.3601887

Weak negative corellation – ‘saltier’ wines seem to contain less alcohol. Does the salt also inhibit the gestation process?

cor(wine$density, wine[, c("chlorides", "total.sulfur.dioxide")])
##      chlorides total.sulfur.dioxide
## [1,] 0.2572113            0.5298813

Positive corellation, higher for “total.sulfur.dioxide”, both chlorides and SO2 increase the density of the wine.

cor(wine$acidity, wine$density)
## [1] 0.2756088

Weak positive corellation, acidity further increases the density of wine.

cor(wine$alcohol, wine$density)
## [1] -0.7801376

Strong negative corellation, alcohol content lowers sugar content and leads to releases of gases, therefore creating a lighter brew and lowering density.

2.20.3 New Findings Concerning Quality

Inspecting the row/column ‘quality’ in the scatterplot matrix, we find particulary high absolute corellation values for the following variables:

cor(wine$quality, wine[, c("volatile.acidity", "fixed.acidity",
            "chlorides", "alcohol", "total.sulfur.dioxide")])
##      volatile.acidity fixed.acidity  chlorides   alcohol
## [1,]        -0.194723    -0.1136628 -0.2099344 0.4355747
##      total.sulfur.dioxide
## [1,]           -0.1747372
  • volatile acidity is negative corellated with quality, as the variable description suggests (“vinegar taste”)
  • fixed acidity also is negatively corellated
  • chlorides (“salts”) seem to have a negative impact on quality
  • higher alcohol content is generally seen as something of higher quality
  • total sulfur dioxide has a negative influence (recall the variable description “becomes noticable over 50ppm”)

2.21 Scatterplot Matrix (facetted by Quality)

We can furthermore imagine, that certain qualities are only relevant for certain flavours of wine. Or we might overlook some non-linear qualities. Quality can be seen as a 7-level factor variable (3-9), so we can add another discrete (color) dimension to our scatterplot to visualize distributions for different levels of quality.

set.seed(1836)
winematrix <- wine[, c(2:15)]
winematrix$quality <- as.factor(winematrix$quality)
ggpairs(data=winematrix[sample.int(nrow(winematrix), 1000), ],
        title="Relationship focussing on wine quality",
        alpha=0.05, colour="quality")

On the diagonal (especially for volatile.acidity, chlorides and density and alcohol) we can clearly see our previous observations: how different quality levels have different means of the respective chemical compound, e.g., how volatile.acidity has a certain local maxima for ‘low quality wine’ (level 3-4) further on the right.

We can, however, also see in column flavor how certain variables seem to be of importance for certain wine flavors and less so for others. For example, citric.acid seems to be positively corellated for classical-dry wines but less so for half dry wines. The same is true for residual sugar, free sulfur dioxide and a few others.

We can plot out the corellation of all of those interesting variables to wine quality for their respective subset of wines of the same flavor with the following formula.

# Show corellation of wine quality with any of a few highlightes variables
# for each wine flavor separately
by(wine, wine$flavor,
    function(w) {
      cor(w$quality, w[, c("volatile.acidity", "fixed.acidity", "citric.acid",
                           "chlorides", "total.sulfur.dioxide", "alcohol",
                           "residual.sugar")])
    }
  )
## wine$flavor: classical-dry
##      volatile.acidity fixed.acidity citric.acid chlorides
## [1,]       -0.1892251    -0.1747645  0.04348309 -0.190533
##      total.sulfur.dioxide  alcohol residual.sugar
## [1,]          -0.07289426 0.457975      0.1654655
## -------------------------------------------------------- 
## wine$flavor: dry
##      volatile.acidity fixed.acidity citric.acid  chlorides
## [1,]       -0.1182325   -0.04137113  0.06397823 -0.2384087
##      total.sulfur.dioxide   alcohol residual.sugar
## [1,]           -0.2598946 0.5512578     -0.1635403
## -------------------------------------------------------- 
## wine$flavor: half-dry
##      volatile.acidity fixed.acidity citric.acid  chlorides
## [1,]       -0.3065855   -0.04305342  -0.1400305 -0.1775522
##      total.sulfur.dioxide   alcohol residual.sugar
## [1,]            -0.158196 0.2469943    -0.00514009
## -------------------------------------------------------- 
## wine$flavor: semi-sweet
##      volatile.acidity fixed.acidity citric.acid  chlorides
## [1,]      -0.01971877    -0.1610847 -0.04354985 -0.2971294
##      total.sulfur.dioxide   alcohol residual.sugar
## [1,]           -0.1896219 0.1595639     0.03847214
## -------------------------------------------------------- 
## wine$flavor: sweet
##      volatile.acidity fixed.acidity citric.acid chlorides
## [1,]               NA            NA          NA        NA
##      total.sulfur.dioxide alcohol residual.sugar
## [1,]                   NA      NA             NA

3 Final Plots and Summaries

3.1 Corellation between Quality and Chemical Properties by Wine Flavor

The following plot visualizes the interesting finding of the last chapter graphically: depending on wine flavor, different chemical qualities play a higher or lower role. Blue signifies positive corellation (positive influence on wine quality), red signifies negative corellation (negative influence on wine quality). Corellations between -0.1 and 0.1 are shown in white as to highlight that they will not be of further investigation.

# here again: corellation of a few highlighted variables with wine quality
# depending on wine flavour
winequality <- wine
# "quality" needs to be a numeric in order to asess corellation
winequality$quality <- as.numeric(as.character(winequality$quality))
winequality <- winequality %>%
     # group by flavour and calculate a bunch of corellations
     dplyr::group_by(flavor) %>%
     dplyr::summarise(cor(quality,alcohol), cor(quality,residual.sugar),
                      cor(quality,chlorides), cor(quality,volatile.acidity), 
                      cor(quality,total.sulfur.dioxide),
                      cor(quality,fixed.acidity), cor(quality,citric.acid)) %>%
     # give each coreallation their own row in the data frame
     tidyr::gather("indicator", "corellation", 2:8)

# palette with 200 steps over shades of blue
b <- colorRampPalette(c("lightskyblue","royalblue","navy"))(200)
# palette with 200 steps over shades of red
r <- colorRampPalette(c("darkred","red2","mistyrose"))(200)
# Plot a tile graphe with the different corellation indicators horizontally
# and the wine flavors vertically arranged
ggplot(winequality, aes(x=indicator, y=flavor)) +
  geom_tile(aes(fill=corellation)) +
  # Background of the tile should be named "Corellation" and reach from
  # red to white to white to blue mapped to -1.0,..,-0.1,0.1,..,1.0
  scale_fill_gradientn(name="Corellation", colours=c(r,"white","white",b),
                       na.value="grey", limits=c(-1,1),
                       breaks=c(-1.0,-0.5,-0.1,0.1,0.5,1.0),
                       values=c(
                           rescale(1:201,to=c(0.0,0.45)),
                           rescale(1:201,to=c(0.55,1.0))
                         )) +
  # label x axis appropriately
  scale_x_discrete(labels=c("Alcohol content", "Residual sugar", "Chlorides",
                            "Volatile acidity", "Total sulfur dioxide", 
                            "Fixed acidity", "Citric acidity")) +
  # add the text into tiles
  geom_text(aes(label=round(corellation,3))) + 
  # labels and titles
  xlab("Indicator") + ylab("Flavor") +
  ggtitle("Influence of certain chemicals on wine quality")

The graph lets us make the following assumptions:

  • Higher alcohol content is associated with better wine quality, especially for dryer wines.
  • Residual sugar is viewed slightly favourable for classical dry wines but not favourable for dry wines; for half-dry or semi-sweet wines, no corellation could be found.
  • Chlorides are generally a bad thing, especially the sweeter the wine.
  • The same roughly applies to Volatile acidity, however, for semi-sweet wines, no corellation can be found.
  • Total sulfur dioxide is corellated with bad wine quality, however, for classical dry wines, no corellation can be established.
  • Fixed acidity and Citric acidity have a small negative effect on some wine flavors, but no overall pattern can be established.

‘No corellation can be found’ does not mean, that no corellation exists - maybe we just do not have the data! – in the final step, we will look behind these corellation values based on wine flavor one last time in more detail.

3.2 Revisiting Distribution of Chemical Compositions

The next graph re-visits the analysis in the beginning of this paper by analyzing a few chemical variables (horizontally) for each wine flavor (vertically). One can see only minor differences:

  • slight left-shift of distribution of total sulfur dioxide for half-dry wine
  • slight left-shift of cidric acid and fixed acid for half-dry and semi-sweet wine

Otherwise, the shape of the distribution does not change – the height, however gets lower, since less wines are available in the sweeter categories. Having that uniformity of distributions assured, we can have more confidence in having compareable samples.

# there is only one "sweet" wine. we will ignore it
winefilter <- wine %>% dplyr::filter(flavor!="sweet")
winefilter$quality <- as.factor(winefilter$quality)

# a bunch of graphs showing the distribution of certain variables
# relating to the chemical qualities of the wine facetted by wine flavor
p1 <- ggplot_hist(
     data=winefilter, x="alcohol", binwidth=0.1,
     xscale=c(8, 14, 0.5*5),
     xlab="Alcohol level in % by volume",
     ylab="Number of wines with that alcohol level",
     facet=~flavor, nrow=4, ncol=1
  )
p2 <- ggplot_hist(
     data=winefilter, x="chlorides", binwidth=0.002,
     xscale=c(0, 0.2, 0.01*5),
     xlab="Chlorides in g/dm³",
     ylab="Number of wines with this amount of chlorides",
     facet=~flavor, nrow=4, ncol=1
  )
p3 <- ggplot_hist(
     data=winefilter, x="total.sulfur.dioxide", binwidth=2,
     xscale=c(0, 400, 10*5),
     xlab="Total Sulfur Dioxide in mg/dm³",
     ylab="Number of wines with this amount of total SO2",
     facet=~flavor, nrow=4, ncol=1
  )
p4 <- ggplot_hist(
     data=winefilter, x="volatile.acidity", binwidth=0.02,
     xscale=c(0, 0.9, 0.05*5),
     xlab="Volatile acidity (acetic acid) in g/dm³",
     ylab="Number of wines with this volatile acidity",
     facet=~flavor, nrow=4, ncol=1
  )
p5 <- ggplot_hist(
    data=winefilter, x="fixed.acidity", binwidth=0.1,
    xscale=c(3.5, 11, 0.5*5),
    xlab="Fixed acidity (tartaric acid) in g/dm³",
    ylab="Number of wines with this fixed acidity",
    facet=~flavor, nrow=4, ncol=1
  )
p6 <- ggplot_hist(
    data=winefilter, x="citric.acid", binwidth=0.02,
    xscale=c(0, 1.4, 0.1*5), 
    xlab="Cidric acid in g/dm³",
    ylab="Number of wines with this citric acidity",
    facet=~flavor, nrow=4, ncol=1
  )
grid.arrange(p1,p2,p3,p4,p5,p6,nrow=1)

3.3 Influence of Chemical Composition on Quality by Wine Flavor

The following graph breaks the distribution further down to show in boxplots the distribution of the selected variable (column) for each quality score (x-axis) and each flavor (row).

Added is the ‘line of best fit’, directly linked to our corellation coefficient from the table in the beginning of this chapter.

We observe the following:

  • Corellation and linear fit are not everything: for example, across all flavors, there are some wines, which are ranked very poorly, but have a higher alcohol content than medium-ranked wines
# now: using boxplots to show the distribution of the 
# variables about chemical composition for any of the
# wine qualities
p1 <- ggplot_boxplot(
     data=winefilter, x="quality", y="alcohol",
     yscale=c(8, 14, 0.5*5),
     ylab="Alcohol level in % by volume", xlab="Quality Score",
     facet=~flavor, nrow=4, ncol=1
  )
p2 <- ggplot_boxplot(
     data=winefilter, x="quality", y="chlorides",
     yscale=c(0, 0.2, 0.01*5),
     ylab="Chlorides in g/dm³", xlab="Quality Score",
     facet=~flavor, nrow=4, ncol=1
  )
p3 <- ggplot_boxplot(
     data=winefilter, x="quality", y="total.sulfur.dioxide",
     yscale=c(0, 400, 10*5),
     ylab="Total Sulfur Dioxide in mg/dm³", xlab="Quality Score",
     facet=~flavor, nrow=4, ncol=1
  )
p4 <- ggplot_boxplot(
     data=winefilter, x="quality", y="volatile.acidity",
     yscale=c(0, 0.9, 0.05*5),
     ylab="Volatile acidity (acetic acid) in g/dm³", xlab="Quality Score",
     facet=~flavor, nrow=4, ncol=1
  )
p5 <- ggplot_boxplot(
    data=winefilter, x="quality", y="fixed.acidity", yscale=c(3.5, 11, 0.5*5),
    ylab="Fixed acidity (tartaric acid) in g/dm³", xlab="Quality Score",
    facet=~flavor, nrow=4, ncol=1
  )
p6 <- ggplot_boxplot(
     data=winefilter, x="quality", y="citric.acid",
     yscale=c(0, 1.4, 0.1*5), 
     ylab="Cidric acid in g/dm³", xlab="Quality Score",
     facet=~flavor, nrow=4, ncol=1
  )
grid.arrange(p1,p2,p3,p4,p5,p6,nrow=1)

4 Reflection

During this project, I learned a lot about plotting with ggplot2, dplyr, tidyr etc. but also about the internal workings of R as a programming language (expression evaluation environments etc.) which I think is somewhat missing from the Data Analyst course.

The things I struggled with most was getting multi-dimensional / -facetted plots with additional cues like whiskers, etc. to work. Also, one can see that for the major part of the analysis, I focus on (linear) corellation while the final plots reveal, that some quadratic relationships (with minima / maxima) are present for some of the chemical compounds, which are hard to spot just looking at corellation. A success was, in my opinion, the idea to differentiate the analysis by wine flavor – for different flavours, indeed, some very different results were obtained.

To enrich the analysis further, one could add more data about those wines, e.g., was the same wine scored by multiple testers? - how much do they disagree and what are the patterns there? - Are other indicators like color, harvestation year or region of the wine indicative?

For this very analysis, based on the premise of focussing highly on corellation, one could of course re-iterate and check other variables again but a quick glimpse on the scatterplot matrix does not reveal any major patterns.

5 References

P. Cortez, A. Cerdeira, F. Almeida, T. Matos and J. Reis. Modeling wine preferences by data mining from physicochemical properties.